Per the source, Balotelli wants to continue his career in Italy, Spain or England but would consider a move to Turkey later on in his career.
The Italian international does not exactly have a long line of clubs desperate to sign him from the Reds considering he scored just one league goal for AC Milan last season.
Balotelli spent last season out on loan but is unlikely to continue his career at Liverpool considering Jurgen Klopp does not have plans for him.
The 25-year-old striker has not been taken along to the pre-season summer camp in the US and has been told to find a new club.
Besiktas are in pursuit of a striker after Mario Gomez declared he will not be returning to the club.
The powerful striker finished last season as top scorer playing a key role in Besiktas lifting the league title and he earned a place back in the Germany national team as a result.